Question: Peggy is moving and is looking to get rid of her record collection. Sammy says that he will buy all of them for 4 dollars each. Bryan is only interested in half of the records but will offer 6 dollars each for the half that he is interested in and 1 dollar each for the remaining half that he is not interested in with the hopes that he can resell them in bulk later. If Peggy has 200 records, what is the difference in profit between Sammy versus Bryan's deal?
Let's think step by step
Sammy is offering to take the whole collection of 200 records and pay Peggy 4 dollars each for them which would net Peggy 200 * 4=800 dollars for her entire record collection.
Bryan is willing to buy Peggy's entire record collection but at two different price points, half at one point and half at another. Half of Peggy's record collection is 200/2=100, which means that 100 records will sell for one price and 100 records will sell for another price.
Bryan is willing to pay more for the half of the record collection that he is interested in so Peggy would net 100 * 6=600 dollars for the first half of her record collection.
For the half of the collection that Bryan is just planning on reselling at a later date, he is willing to offer Peggy 100 *1=100 dollars to take off of her hands.
In total Bryan is willing to offer Peggy 600+100=700 dollars for her entire record collection.
If Sammy is offering 800 dollars to buy Peggy's entire record collection and Bryan is offering 700 dollars for Peggy's entire record collection, then Peggy's net profit would be 800-700=100 dollars more by taking Sammy's deal instead of Bryan's deal.
The answer is 100

Question: Hasan is packing up his apartment because he’s moving across the country for a new job. He needs to ship several boxes to his new home. The movers have asked that Hasan avoid putting more than a certain weight in pounds in any cardboard box. The moving company has helpfully provided Hasan with a digital scale that will alert him if a package is too heavy. Hasan is in the kitchen, and he fills a cardboard box with 38 dinner plates. When he checks the box, the scale reports his box is too heavy. Hasan knows each of his plates weighs 10 ounces. He removes a single plate from the box and checks the movers’ scale again. The scale reports his box is still too heavy. Hasan repeats the process again and again. When he has removed enough plates, the movers’ scale shows the box is now an acceptable weight for shipping. Hasan deduces that each shipping box can hold 20 pounds before the scale says the box is too heavy.  How many plates did Hasan need to remove from the shipping box?
Let's think step by step
Let x be the number of plates removed from the box.
Hasan figured out the movers' weight limit was 20 pounds. Since a pound is equal to 16 ounces, each box can hold 20 * 16, or 320 ounces.
Each plate weighs 10 ounces, so the weight of the plates in the box after Hasan removes enough plates to satisfy the movers' weight limit is (38 - x) * 10 ounces
Since these two values are equal, we can write the equation (38 - x) * 10 = 320.
Dividing both sides by 10 leaves 38-x = 32.
Adding x to both sides gives 38 – x + x = 32 +x, or, 38 = 32 +x
Subtracting 32 from both sides gives the value of x, which is the number of plates removed from the box, 38 -32 = 32 + x – 32, or, 6 = x
The answer is 6

Question: Angelo and Melanie want to plan how many hours over the next week they should study together for their test next week. They have 2 chapters of their textbook to study and 4 worksheets to memorize. They figure out that they should dedicate 3 hours to each chapter of their textbook and 1.5 hours for each worksheet. If they plan to study no more than 4 hours each day, how many days should they plan to study total over the next week if they take a 10-minute break every hour, include 3 10-minute snack breaks each day, and 30 minutes for lunch each day?
Let's think step by step
Angelo and Melanie think they should dedicate 3 hours to each of the 2 chapters, 3 hours x 2 chapters = 6 hours total.
For the worksheets they plan to dedicate 1.5 hours for each worksheet, 1.5 hours x 4 worksheets = 6 hours total.
Angelo and Melanie need to start with planning 12 hours to study, at 4 hours a day, 12 / 4 = 3 days.
However, they need to include time for breaks and lunch. Every hour they want to include a 10-minute break, so 12 total hours x 10 minutes = 120 extra minutes for breaks.
They also want to include 3 10-minute snack breaks, 3 x 10 minutes = 30 minutes.
And they want to include 30 minutes for lunch each day, so 120 minutes for breaks + 30 minutes for snack breaks + 30 minutes for lunch = 180 minutes, or 180 / 60 minutes per hour = 3 extra hours.
So Angelo and Melanie want to plan 12 hours to study + 3 hours of breaks = 15 hours total.
They want to study no more than 4 hours each day, 15 hours / 4 hours each day = 3.75
They will need to plan to study 4 days to allow for all the time they need.
The answer is 4

Question: A curry house sells curries that have varying levels of spice. Recently, a lot of the customers have been ordering very mild curries and the chefs have been having to throw away some wasted ingredients. To reduce cost and food wastage, the curry house starts monitoring how many ingredients are actually being used and changes their spending accordingly. The curry house needs 3 peppers for very spicy curries, 2 peppers for spicy curries, and only 1 pepper for mild curries. After adjusting their purchasing, the curry house now buys the exact amount of peppers they need. Previously, the curry house was buying enough peppers for 30 very spicy curries, 30 spicy curries, and 10 mild curries. They now buy enough peppers for 15 spicy curries and 90 mild curries. They no longer sell very spicy curries. How many fewer peppers does the curry house now buy?
Let's think step by step
The curry house previously bought 3 peppers per very spicy curry * 30 very spicy curries = 90 peppers for very spicy curries.
They also bought 2 peppers per spicy curry * 30 spicy curries = 60 peppers for spicy curries.
They also bought 1 pepper per mild curry * 10 mild curries = 10 peppers for mild curries.
So they were previously buying 90 + 60 + 10 = 160 peppers.
They now buy 2 peppers per spicy curry * 15 spicy curries = 30 peppers for spicy curries.
They also now buy 1 pepper per mild curry * 90 mild curries = 90 peppers for mild curries.
So they now buy 30 + 90 = 120 peppers.
This is a difference of 160 peppers bought originally - 120 peppers bought now = 40 peppers.
The answer is 40

Question: Sam works at the Widget Factory, assembling Widgets. He can assemble 1 widget every 10 minutes. Jack from the loading dock can help assemble widgets when he doesn't have anything else to do. When he helps, they put together 2 complete widgets every 15 minutes. Recently the factory hired Tony to help assemble widgets. Being new to the job, he doesn't work as fast as Sam or Jack. Yesterday Sam worked for 6 hours before he had to leave work early for a dentist appointment. Jack was able to help out for 4 hours before he had to go back to the loading dock to unload a new shipment of widget materials. Tony worked the entire 8-hour shift. At the end of the day, they had completed 68 widgets. How long does it take Tony to assemble a Widget, in minutes?
Let's think step by step
Sam completes a widget every 10 minutes.
When Jack helps they finish 2 in 15 minutes. Sam has finished 1 widget and has begun working on another one, and Jack finishes the second one at 15 minutes. So it takes Jack 15 minutes to complete a widget.
Sam worked for 6 hours yesterday, so he was able to complete 6 hours * 60 minutes per hour / 10 minutes per widget = 36 widgets.
Jack worked for 4 hours, so he was able to complete 4 hours * 60 minutes per hour / 15 minutes per widget = 16 widgets.
Sam, Jack, and Tony were able to complete 68 widgets together. So of those, Tony personally completed 68 widgets - 36 widgets - 16 widgets = 16 widgets.
It took Tony 8 hours to complete those 16 widgets, so he takes 8 hours * 60 minutes per hour / 16 widgets = 30 minutes per widget.
The answer is 30

Question: Ellie went to visit a circus with Sarah and they both got lost in the house of mirrors. They have to travel through the house of mirrors a few times before they finally get out and when they leave, they discuss how many times they've seen their own reflections. Sarah says that every time they were in the room with tall mirrors, she saw her reflection 10 times and every time they were in the room with wide mirrors, she saw her reflection 5 times. Ellie says that every time they were in the room with tall mirrors, she saw her reflection 6 times and every time they were in the room with wide mirrors she saw her reflection 3 times. They both passed through the room with tall mirrors 3 times each and they both passed through the room with wide mirrors 5 times each. In total, how many times did Sarah and Ellie see their reflections?
Let's think step by step
In the rooms with tall mirrors, Sarah saw her reflection a total of 10 reflections * 3 passes = 30 times.
In the rooms with wide mirrors, Sarah saw her reflection a total of 5 reflections * 5 passes = 25 reflections.
So Sarah saw her reflection a total of 30 + 25 = 55 times.
In the rooms with tall mirrors, Ellie saw her reflection a total of 6 reflections * 3 passes = 18 times.
In the rooms with wide mirrors, Ellie saw her reflection a total of 3 reflections * 5 passes = 15 times.
So Ellie saw her reflection a total of 18 + 15 = 33 times.
Therefore, Sarah and Ellie saw their reflections a total of 55 + 33 = 88 times.
The answer is 88

Question: Janet hires six employees. Four of them are warehouse workers who make $15/hour, and the other two are managers who make $20/hour. Janet has to pay 10% of her workers' salaries in FICA taxes. If everyone works 25 days a month and 8 hours a day, how much does Janet owe total for their wages and taxes for one month?
Let's think step by step
First figure out how many hours each worker works per month by multiplying the number of days they work by the number of hours a day they work: 25 days * 8 hours/day = 200 hours
Then calculate how much one warehouse worker makes per month by multiplying their hourly rate by the number of hours they work: 200 hours * $15/hour = $3000
Then multiply that number by 4 to find out how much all the warehouse workers make: $3000/worker * 4 workers = $12,000
Now multiply the hours each manager works (also 200) by their hourly wage to find out how much one manager makes per month: 200 hours * $20/hour = $4,000
Now multiply one manager's wages by the number of managers (2) to find their total wage amount: $4,000/manager * 2 managers = $8,000
Now add the wages for the managers and the workers to find the total cost of the wages: $8,000 + $12,000 = $20,000
Now multiply the total wage bill by 10% to find how much the FICA taxes are: $20,000 * .1 = $2,000
Now add the total wage bill to the total tax amount to find the grand total: $2,000 + $20,000 = $22,000
The answer is 22000

Question: Alec is running for Class President. He thinks that if he can get three-quarters of the class to vote for him then there is no chance anyone else can beat him. Half of the class have already said they will vote for him but out of the remaining students, only 5 have said they are thinking about voting for him. He surveys the students who are thinking about voting for someone else, and changes his flyers to reflect the issues these students are concerned about. This results in a fifth of these students saying they'll vote for him. If Alec's class has 60 students and everyone who said they will vote for him does so, how many more votes does Alec need to reach his goal number of votes?
Let's think step by step
To calculate Alec's goal number of votes, we need to know that 60 students / 4 = 15 students is equal to one-quarter of the class students.
Alec's goal is therefore 15 students * 3 quarters = 45 votes.
Half of the class said they will vote for him, so there are already 60 students / 2 = 30 votes.
Another 5 students are thinking about voting for him which leaves a total so far of 30 + 5 = 35 votes.
This means there are 60 students - 35 voting for Alec = 25 students not voting for Alec.
A fifth of these decided to vote, so this is a further 25 students / 5 = 5 votes.
Alec is therefore receiving a total of 35 + 5 = 40 votes.
So he has missed his goal by 45 goal votes - 40 actual votes = 5 votes.
The answer is 5
